question 4 5 6 Determine whether the following statements are true or false.Justify your answer with brief explanations or counterexamples.(1).All groups of order 9 are isomorphic to each other.(2).The set of positive real numbers forms a monoid under multiplication.(3).If G is a group whose order is a prime number, then G is a simple group.Suppose that f: G → G' is a monomorphism, G is a non-trivial group andG' is non-abelian. Then G can not be abelian.(4).(5).(6).under the action.If every subgroup of G is a finite group, then G must be a finite group.Let Z₁4 acts on a set X with 3 elements. Then there are at least 2 orbits14

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Answered: (4). Suppose that f: G→ G' is a…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.4: Cyclic Groups

Problem 16E: For an integer n1, let G=Un, the group of units in n that is, the set of all [ a ] in n that have...

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(4). Suppose that f: G→ G' is a monomorphism, G is a non-trivial group and G' is non-abelian. Then G can not be abelian. (5). If every subgroup of G is a finite group, then G must be a finite group. (6). Let Z14 acts on a set X with 3 elements. Then there are at least 2 orbits under the action.